Should fields consider running Airsoft like a hockey game, with time penalties for rules violations? Since many Airsoft missions run about an hour (same as a hockey game), I think it could work. The refs would wear all black instead of B&W stripes and there would be any number of them throughout the field where they could observe game behavior. When they see a violation, they would write it down and wait for a lull in fighting, then penalize the player responsible with X number of minutes at their respawn.
Cheating, swearing at opponents (unsportsmanlike conduct), demanding opponents call hits (unsportsmanlike conduct), blind firing, abuse of game props, illegal contact, shooting too closely, illegally entering the game (leaving respawn too early) would all be given two minute (minor), four minute (double minor) or five minute (major) penalties. Cursing at refs, field owners, or instigating fighting would all be ten minute penalties (misconduct) in addition to any other penalty.
Players would not need to wear numbers as refs would not stop game flow, they simply walk over and tell a player they have a penalty and how long it is. Refs would communicate on dedicated channels and also be trained in first aid and safety.